ON OPTICAL THEORIES. 191 
and put 
—(--—)=- : : : . (42 
A\k ky ; me 
In Eisenlohr’s account of Cauchy’s work it is assumed at first that 
the normal waves travel with the same velocity as the transverse, and 
then the solution is modified by putting for X,,, \’, the wave lengths of the 
normal waves, the values —1,,/ —1 and — 1./ —1. This modifies 
$,, and 9”, the angles of refraction and reflexion of the normal waves, so 
that their sines become imaginary, while cos @,, is real and negative, 
cos ¢” real and positive. l 
A difference of phase is thus produced, determined by the following 
equations :— 
tan e =p tan (¢ — ¢’), 
tan e’= p tan (¢ + ¢’), 
where 
m'’ — m,, 
[P m''m,, — 1’ 
= a8 
Poet J( + rary)? 
x2 
MW — 1 eS eee I 
m™ / ( + yr ain = 
Jamin’s results show that p is very small; hence we may write 
Pp 
and 
r r 
pale i qty, 
where w is small, and then 
2u sin ¢ 
t/ (# + sin? ¢) 
Cauchy puts p = « sin ¢, when ¢ is a small constant. Hence we must 
suppose that ¢ is great compared with ¢. 
Lorenz and Lord Rayleigh have both pointed out the serious objec- 
tion to be made to the theory in this form. The equation to determine © is 
ao eo mz ao and the medium will be essentiall unstable 
dz? dy? G diz’ ~ ; 
Moreover, if i be a constant, ¢ varies inversely as A, and chromatic effects 
near the polarising angle should be much more marked than they are. 
T have, however, given an account of Eisenlohr’s paper mainly because 
of another suggestion he makes, which renders it very nearly identical 
with Green’s. He suggests that the normal or pressural waves may 
yanish ‘by a sort of total reflexion, their velocity being very great com- 
pared with that of the transverse waves.’ So that we have \,, and d// 
very large instead of imaginary, and from this he finds 
( (43) 
Ser Secrane DHidd Vilonla dulttw-e'sneut) OAR 
4/ 
This vanishing by a sort of total reflexion is exactly Green’s theory, for 
